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A163849 Primes p such that the difference between the nearest cubes above and below p is prime. 1

%I

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,223,227,229,233,239,241,251,257,263,269,271,

%U 277,281,283,293,307,311,313,317,331,337,733,739,743,751,757,761,769,773

%N Primes p such that the difference between the nearest cubes above and below p is prime.

%C There is a sequence A048763(A000040(n)) = A145446(n) of nearest cubes above the primes and a sequence A048762(A000040(n)) of nearest cubes below the primes.

%C If the difference A145446(n) - A048762(A000040(n)) is prime, then A000040(n) is in this sequence.

%H G. C. Greubel, <a href="/A163849/b163849.txt">Table of n, a(n) for n = 1..2500</a>

%e The difference of cubes 6^3 - 5^3 = 91 = 7*13 is not prime, so the primes larger than 5^3 = 125 but smaller than 6^3 = 216 are not in the sequence.

%t f[n_]:=IntegerPart[n^(1/3)]; lst={};Do[p=Prime[n];If[PrimeQ[(f[p]+1)^3-f[p]^3], AppendTo[lst,p]],{n,6!}];lst

%Y Cf. A111252, A145446.

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 05 2009

%E Edited by _R. J. Mathar_, Aug 12 2009

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Last modified January 24 10:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)